An evaluation method and clustering of credibly behavior of customers using AHP and fuzzy neural networks

Abstract

Decision making on allocation of limited financial resources and determining the service quality level and facilities to the customers is an important issue for banking industries and financial enterprises. In this research by using neural networks, customer’s credibly behavior is modeled and clustered in order to optimize the allocation of financial resources and enhance the quality of banking services. By using Analytic Hierarchy Process (AHP), weighting coefficients of each input variable is determined and then these coefficients are used as primarily weights in fuzzy neural networks (FNN). This approach has increased training speed and accuracy of FNN considerably. Also the customers credibly behavior is predicted by using neural networks clustering models. The fuzzy neural networks model with the same data is also carried out without using AHP weights. The comparison of both approaches show the fuzzy neural networks clustering models with AHP weightings is more accurate with higher prediction speed. The model is implemented for a real application of Iranian National Bank. The case study shows 98% increase in prediction speed and 12% increase in accuracy.

Keywords

Banking industry customer credibly fuzzy neural networks AHP

1 Introduction

Decision making sciences have always been engaged with human behavior and the formation of new enterprises and organizations where high changes in environmental factors have been improved [1]. As of now, numerous researches have been developed in this area dealing with the better and more accurate models to improve the decision makingprocesses and to help the decision maker.

One of the main activities of the banks and financial organizations is credits assignment to the customers. For a correct decision one should know the level of validity and ability of the customers’ reimbursement of the interest and original loans, in order to reduce the level of credibly risks. One way to reduce the credibly risks is to design a credit rating system for those who receive bank facilities. The main core of this system is a rating model that evaluates customers’ credibly [2]. With such model, the customer credibly degree is determined and on that basis the amount of fund granted to each customer is decided. However, there is always some degree of risk on reimbursement of loans, which can affect the financial resources of a bank. The degree of customer credibly can be measured by the 5C model. The 5C model criterion includes Character, Capacity, Capital, Collateral, and Conditions of Economy. Character refers to the degree of customers’ effort in paying back their loans. Capacity is a conceptual criterion for evaluation of the capability of customers in usage of the loan and also reimbursement of the interest and the original loan. Capital can be measured by referring to customers’ financial status using financial criterion. Collateral is the assets with which customers guarantee loan or other facilities obtain. Economical condition evaluates the general trend and economical changes, which affect the ability of the customers to reimburse their loan [3].

Customer credibly evaluation can be performed by evaluators or experts. This method however has disadvantages such as its higher costs, the process is time-consuming, as well as shortage of evaluators and the high number of cases to be evaluated. Application of Information and Commutation Technology (ICT) in banking system provides opportunities as well as challenges for banks. It is possible to design various models to evaluate customer credibly by using scientific approaches instead of intuitive judgments. Such models can differentiate between the customers’ excellent, good, and poor behavior in a short time and with a reasonable cost. In this research while the quantitative and qualitative factors affecting banks’ customer credibly evaluation are identified, a model is developed to evaluate and allocate facilities to customers.

Financial institutions try to use knowledge techniques and means for an automatic decision in order to improve the customer evaluation and loan process and help managers in their decisions and predictions. Techniques such as neural networks and Expert Systems (ES) are used for these purposes. ES is usually used for a few financial decision making issues, and some other financial issues like customers credibility clustering, risk evaluation, and coloration forecasting, are beyond the capability of ES. Shortcomings of ES also include difficulties in planning and maintenance of a system, time consuming process, complexity of extracting knowledge from human expertise, and lake of intellectuality to establish rules. These limitations may result in difficulties in analyzing the financial problems. In recent years, intelligent systems, as one of the advance tools in various science fields, are used for optimization and forecasting. Neural networks as one of these systems are applied in financial aspects including granting customer credit. Based on human understanding, and fast and accurate learning, Fuzzy Neural Networks (FNN) through simulating processes, are capable of generating suitable answer to such problems, even when the data are not complete. Fuzzy theory is used in this paper to incorporate the uncertainty of human thoughts in modeling. Also in evaluating customer credibly, defining the relation and movement of a set of variables with another set is very important. For this purpose, the NN models are ideal since they can analyze and compare various sets of variables simultaneously, which is beyond the human ability [4]. To validate the research, a case study is used to perform a comparative study on ANN and AHP versus ANN. The neural network dimension for both conditions in the study is considered identical and for the second case, AHP structure and weights are used for designing neural network.

The rest of the paper is structured as follows. The related literature is presented in Section 2. The application of NN in credit approval is presented in Section 3, including identification and calcification of the criteria, statistical population and sampling, transforming the data for NN, application of AHP to determine the NN primary weights, and selection of training and testing data sets. Selection a suitable architecture for network is presented in Section 4. The data for NN training considers in Section 5. Test and execution of network is presented in Section 6. Section 7 presents the numerical results, and ultimately Section 8 ends with the conclusions and recommendations for further research.

2 Literature review

Granting bank facilities is vitally important from economic points of view. The importance is because increasing the amount of capital quantities leads to economical development [5]. But allocating these facilities, banks may face a crucial problem of credit risk, which is the probability of unpaid loans by customers. This risk is the main reason of banks’ financial crisis. To manage the credit risk, various ways are suggested. One of them is designing credit degree measurement system for the receivers of bank facilities [2]. Evaluating customers’ credibly is also a complicated issue in financial activities. Number of factors and complexity of financial, economical, and behavioral relations make customers’ credit evaluation difficult. On the other hand, evaluating processes should be done in a limited time framework. If the process becomes time consuming, the operation will face delay, which causes additional costs. Also, lack of accuracy in evaluation may lead to wrong decisions and big losses. Time limitation and necessity of accuracy in evaluating raise complexity of the issue dramatically [4]. According to Altman [6], rating systems of customers’ credibly are divided into three groups: judgment systems, statistical techniques and intelligent systems [6]. Judgment systems are costly and time consuming. The system’s efficiency decreases when the number of orders is too many and has to be judged by limited experts. When it comes to statistical methods, each technique needs especial assumptions. If these assumptions are fainted or ignored in any statistical techniques, the output accuracy and validation raise doubts. When decision making rules are explicit and information is valid, expert systems could be a great help to solve the problems. But institutes’ loan allocation rules are often not clear or the information needed either does not exist or is incomplete and inaccurate. In this situation, using NN is a suitable option to assess customers’ credibly [7]. One of the most profitable implementations of neural networks is performed in Chasse bank of United States. In this bank, customers’ credit factors are used in strategic planning in order to decrease losses of loans and facilities. On these bases, most of the Chase bank transactions are categorized to one of the following conditions: good, poor or average [8].

Kivijari and Tuominen [9] using a real case show how a computer based system can support investment management process efficiently [9]. This system, in each level of investment process, attempts to use human judgment with computer assistance which accepts theoretical and practical data at the same time. In this system after identifying and calcifying the criteria, they are weighed by the AHP approach and a software is developed to assess customers’ credit.

Based on Penster Stock’s [10] study [10], experience of granting facilities, in banks and financial institutions reveals a four step decision makingprocess:

Should we assign credit to facilities demandant?

In which time period should the fund be assigned to a customer?

Is there any necessity what so ever to intervene the process?

In the case of intervening, how should the deal be conducted?

Thomas [11] considered the statistical and operational research based techniques such as credit scoring and behavioral scoring to support the decision about granting credit to consumers [11]. F. Group separation idea in a population was primarily proposed by Fisho in 1936 [12]. Altman developed first credit request evaluation system by using five criteria [13]. In 1963, Mayzer and Honarji [14] introduce an audit multivariate analysis to rank customers’ credibly. In 1967 for the first time, Moore and Koln pointed out that the relationship between variables and criteria changes over time. Altman [6] presented a score model; using audit multivariate analysis to rank companies [6]. The second generation of this model was introduced in 1977 by Altman, Holadman, and Narayanan. In 1980, logistic regression and linear programming was applied to assess customers’ credit [13].

Artificial intelligence techniques are seeking ways to increase companies’ profit from a particular customer instead of reducing customers’ chance with inappropriate request [15]. One of the obstacles in granting facilities in Iran credits market is the regulations of collateral receiving or the liquidity brought by customers. Data analysis in a study indicates 75% of applicants believe the barriers to avail bank facilities are collateral receiving regulations and inflexibility of the evaluation criteria. Also around 95% of respondents consider the credit assessment process too long [13].

Theoretical and empirical framework for evaluating bank risk-based capital standards are developed by Grenadier and Hall [16]. They considered a pricing methodology for loans subject to default risk and the returns on the loans. Treacy and Carey [17] considered the internal credit risk rating systems at the 50 largest US banking organizations to study the relationships between uses of ratings, different options for rating system design, and the effectiveness of internal rating systems [17]. Lopez and Saidenberg [18] proposed a panel data approach to evaluate the methods for credit risk models based on cross-sectional simulation [18]. Yang et al. [19] developed a knowledge-base system for bank loan risk management and evaluated the quality of internal supervision and auditing in bank loan processing [19]. The importance of making loan loss provisioning an integral part of bank capital regulation is examined by Laeven and Majnoni [20]. They analyzed the cyclical patterns of bank loan loss provisions in the commercial banks in different geographical areas of the world.

Emery and Cantor [21] examined the differences in loan and bond default rates among US non-financial corporates and indicated that the differential in default rates is due to the fact that issuers default on their bonds but avoid bankruptcy and avoid defaulting on their loans [21]. Kanagaretnam et al. [22] examined bank managers’ discretionary decisions over the estimating loan loss provisions to convey information about their banks’ future prospects and used four factors namely bank size, earnings variability, investment opportunity, and degree of income smoothing to explain banks’ signaling through loan loss provisions [22]. Anandarajan et al. [23] developed a stochasticfrontier model to investigate the inefficiency of the Loan Loss provision decisions of bank managers [23]. Dermine and Carvalho [24] used mortality analysis to defaulted bank loan recovery rates and calculated interest rate risk and credit risk provisions over time [24]. Dinh and Kleimeier [25] proposed a credit scoring model for Vietnamese retail loans to achieve the strategic objectives of the bank [25].

Graham et al. [26] investigated how loan contracts are affected by the changes in credit risk and the uncertainty about the firm’s financial information that follow a restatement, They showed that the restatement increases the credit risk and heightened informational issues and may affect the structure of lenders in a loan [26]. Kang and Liu [27] examined the efficiency of banks’ loan decisions in Japanese banks and analyzed valuation effect of loan announcements on the borrowing firms and the lending banks, They showed that the bank loan announcements can lead to wealth transfer from lending banks to borrowing firms [27]. Foos et al.[28] investigated the effect of loan growth on riskiness of banks based on bank scope data from more than 16,000 individual banks in 16 major countries and indicated that loan growth can lead to an increase in loan loss provisions [28]. Fang et al. [29] examined the relation between borrowing firms’ alliance activities and non-financial firms’ bank loan financing and indicated that borrowing firms actively involved in alliance activities experience low cost of bank loans [29]. Majeske and Lauer [30] developed a probability model to evaluate the predictive validity and used the Bayesian decision model to classify the bank loan approval in the context of personal credit scoring and bank loan applications [30].

Considering credits market conditions and credit ranking models, this study predicts behavioral patterns and loan reimbursement in Iranian banks. Also it is tried to develop a customers’ credit ranking system. In the first step, effective variables to customers’ credit behavior are identified and classified. Then, the weight of each criterion is determined with AHP. NN models are designed to rank customers’ credit. Finally, an NN is designed and run with AHP weighting. The results show the efficiency of AHP’s weights in comparison with stochastic weights.

3 Applying NN for credits approval

Intelligent NN’s are suitable tools for complicated environments that are unstructured and in some cases require pattern recognition, while the data are either crashed or incomplete. In banking systems when a group of ordinary financial employees is responsible for approval of credits and the limit of credit allocation, the process would be time consuming and requires a lot of work.

Nevertheless, an NN system could use the customer information as an input vector and examine the actual decisions of the credit analyzer of an institute as a proper output vector. In fact, the objective of this system is imitating the human being decision making behavior in credit granting. Also the system should be able to face the diverse input data without the need to change them to a standard form. The general process of using ANN in credit allocation problem is as follows:

Collecting suitable and effective data.

Classifying data into training and testing sets.

Transforming data into a proper input data for the network.

Selecting a suitable architecture for NN.

Training, testing, and executing the network.

Based on the objective of the research various type of ANN can be used. One of the most widely used is Multilayered Feed forward Neural Network (MFNN). These networks are examples of supervised training NN. Based on recent studies, more than fifty percent of reported practical studies of MFNN used the back propagation training algorithm rules [31]. This type of NN has vast application in various aspects of management like forecasting, clustering, and modeling. MFNN is also suitable for problems which include relationship between sets of input/outputs.

In this study, by combining ANN and fuzzy logic, a fuzzy system is developed, which has a learning ability. In this method, in each training round during forward movement the outputs of groups are determined in an ordinary manner and the process is continued until the last layers. Then, by comparing the actual output values with desired values, using least squire error method, the amount of error is calculated. In a backward path, error ratio is distributed on the condition’s parameters and by using error descending slope its value is corrected. Various structures for implementation of a fuzzy system using neural networks are proposed. One of the powerful structures is called Adaptive Neural Fuzzy Inference Systems (ANFIS), which is developed by Jarrs [32]. The architecture of ANFIS is as shown in Fig. 1

Fig.1

Architecture of ANFIS.

In this network, input and output values and weights are in fuzzy form. The ANFIS training of back propagation is wrong. In this approach by using a descending sharp slope algorithm, the error values will be distributed on inputs and the parameters will be corrected. The main difference between FNN and ANN is that in FNN the input and output values, and weights are defined in fuzzy.

3.1 Identification and classification of effective criterion of customer credit clustering

For better understanding of the evaluation and clustering of customer’s credit in Iran, a number of interviews have been carried out with some experts from a few banks and financial institutes. Comparing the gathered information, and studies of banks and financial institutes from other countries, shows that Iranian banks and financial institutes, unlike other countries, do not have a comprehensive and complete model for customer credit evaluation and clustering.

As the interviewed experts suggest, in the absence of codified rules in this field, the ground is prepared for influencing the approval of customer’s credits that may not have necessary qualification. In the second stage of this study, to collect and complete the data, two separate questionnaires were provided to the experts and the managers. In the first questionnaire according to the view of our interviewer and primarily analysis the criteria is divided into five groups and were placed in separate tables. Based on the Likert scale, the view of experts and managers on the necessity and the importance of each criterion was recorded. Figure 2 shows the clustering of these criteria. The reliability of them is verified on the basis of the experts’ viewpoint, and their validity is verified by using Cronbach’s Alfa (=0.89) with r = 0.92.

Fig.2

Calcification of criterion and effective factors on clustering of customers’ credit.

3.2 Statistical population and sample

To evaluate the NN of the Iranian National Bank, a sample of 400 experts from various branches of the banks has been used. These 400 branches included 10 samples of 40 banks from Tehran, Isfahan, Mashhad, Shiraz, Ahvaz, Kerman, Yazd, Semnan, Tabriz, and Zahedan cities. For data gathering, a questionnaire with three sections was designed. In the first section, the demographic information of employees like place of work, service background, education, marriage status, and the amount of salary and income was asked. In the second section of the questionnaire, the information on main factors affecting the clustering of customer credibly, such as managerial criterion, financial and economical criterion, customer characteristics, carrier history and education, was asked. The importance of each factor is measured through a Likert scale. The third section includes the level of effect of each secondary factor on the mainfactors.

3.3 Data transformation to a suitable input format for NN

NN inputs’ intervals are generally 0 to 1 and or 1 to –1. Each field in the database should be entered to one or few network inputs and in an adequate amount. The reason for transforming the information into a suitable input format for network is to find a way to design the database on a suitable format for NN input. These inputs can be fuzzy, deterministic, and or probabilistic [33]. In this article, to transform the data to suitable inputs for NN, the five Likert scales for each factor are used based on Table 1 andFig. 2.

Table 1
Options weight and abbreviation

Options Options weight Abbreviation

Excellent (0.75,1,1) E

Good (0.5,0.75,1) G

Fair (0.25,0.5,0.75) F

Poor (0,0.25,05) P

Very Poor (0,0.,0.25) VP

Options	Options weight	Abbreviation
Excellent	(0.75,1,1)	E
Good	(0.5,0.75,1)	G
Fair	(0.25,0.5,0.75)	F
Poor	(0,0.25,05)	P
Very Poor	(0,0.,0.25)	VP

3.4 Using AHP for determining NN’s primary weights

AHP is one of the most popular multi-criteria decision making (MCDM) method in solving complex decision problems. Initially AHP was introduced by Saaty [33] to solve the economical-social decision problems [33]. AHP is used as a powerful tool in a variety of decision problems. Surveys of developments and applications of AHP method include safety management and risk assessment [34], Supplier selection [35], airline industry [36], natural resource management [37], analysis of electricity supply chain [38], facility layout design [39], and industrial machinery [40].

In the bank area Arbel and Orgler [41] considered the application of AHP methodology to evaluate the bank merger and acquisition strategy [41]. Haghighi et al. [42] proposed a fuzzy AHP method to investigate the impact of 3D e-readiness, namely the industry e-readiness, organizational e-readiness and macro environmental e-readiness on e-banking development [42]. Che et al. [43] proposed a fuzzy AHP and DEA approach for making bank loan decisions for small and medium enterprises in Taiwan [43]. Recently Ishizaka and Nguyen [44] presented a fuzzy AHP method to investigate criteria selection for bank accounts amongstudents [44].

AHP is a graphical demonstration of a complicated actual problem. In AHP method, first the problem is converted to a hierarchic structure and then the alternatives are ranked based on the decision maker’s judgments. The overall decision goal stands at the top level, criteria and sub-criteria lie in the next levels, and the lowest level consists of all possible alternatives. In this process, to compare the options, quantitative and qualitative targets are measured as pairs.

To calculate primary weights in NN, the weights from the questionnaire are used. The result is a pair comparison table. Using the $(\frac{w_{i}}{w_{j}})$ fraction, this table compares individual elements of each level in relation to elements of other levels. Then by using AHP rules and Expert Choice software, final weight of each criteria, sub-criteria and options relevant to each other are determined. These weights are shown in Table 2.

Table 2
The NN weights for first and second levels

Management M = (0.1,0.2,0.3) Financial E = (0.25,0.3,0.35) Customer characteristics C = (0.2,0.25,0.3) Feasibilities factors F = (0.1,0.15,0.2) Carrier and education background J = (0.15,0.2,0.2) Main factors Secondary

(0.2,0.25,0.3) (0.25,0.3,0.35) (0.2,0.3,0.4) (0.1,0.15,0.2) (0.1,0.2,0.3) J₁

(0.25,0.3,0.35) (0.3,0.4,0.5) (0.25,0.35,0.45) (0.15,0.2,0.25) (0.15,0.25,0.35) J₂

(0.3,0.35,0.4) (0.35,0.4,0.45) (0.3,0.4,0.5) (0.25,0.3,0.35) (0.25,0.3,0.35) J₃

(0.25,0.3,0.35) (0.3,0.35,0.4) (0.25,0.3,0.35) (0.2,0.25,0.3) (0.2,0.25,0.3) J₄

(0.2,0.25,0.3) (0.15,0.2,0.3) (0.1,0.15,0.2) (0.15,0.2,0.25) (0.15,0.2,0.25) J₅

(0.1,0.15,0.2) (0.05,0.1,0.15) (0.05,0.15,0.2) (0.1,0.15,0.2) (0.1,0.15,0.2) J₆

(0.1,0.15,0.2) (0.05,0.1,0.15) (0.1,0.15,0.2) (0.05,0.1,0.15) (0.05,0.1,0.15) J₇

(0.2,0.3,0.4) (0.2,0.3,0.4) (0.25,0.35,0.45) (0.2,0.3,0.4) (0.3,0.4,0.5) J₈

(0.4,0.5,0.6) (0.15,0.25,0.35) (0.2,0.3,0.5) (0.3,0.4,0.5) (0.2,0.3,0.4) F₁

(0.4,0.5,0.6) (0.25,0.35,0.45) (0.2,0.35,0.4) (0.35,0.45,0.55) (0.25,0.3,0.35) F₂

(0.5,0.6,0.7) (0.2,0.3,0.35) (0.25,0.3,0.35) (0.4,0.5,0.6) (0.2,0.3,0.4) F₃

(0.4,0.5,0.6) (0.25,0.35,0.45) (0.2,0.3,0.4) (0.4,0.5,0.6) (0.4,0.45,0.5) F₄

(0.45,0.5,0.55) (0.35,0.45,0.55) (0.3,0.4,0.5) (0.4,0.5,0.6) (0.35,0.4,0.45) F₅

(0.6,0.65,0.7) (0.4,0.5,0.6) (0.5,0.6,0.7) (0.6,0.7,0.8) (0.4,0.5,0.6) F₆

(0.5,0.55,0.6) (0.15,0.2,0.25) (0.2,0.3,0.4) (0.2,0.3,0.4) (0.35,0.45,0.55) F₇

(0.6,0.7,0.8) (0.25,0.35,0.45) (0.3,0.4,0.5) (0.4,0.5,0.6) (0.3,0.4,0.5) F₈

(0.1,0.2,0.3) (0.15,0.25,0.35) (0.2,0.3,0.4) (0.15,0.3,0.35) (0.2,0.3,0.35) C₁

(0.2,0.3,0.4) (0.2,0.3,0.4) (0.25,0.3,0.35) (0.2,0.25,0.3) (0.2,0.25,0.3) C₂

(0.15,0.25,0.35) (0.25,0.35,0.4) (0.3,0.4,0.5) (0.25,0.35,0.45) (0.2,0.3,0.4) C₃

(0.2,0.3,0.4) (0.1,0.2,0.3) (0.2,0.3,0.4) (0.1,0.2,0.3) (0.15,0.25,0.35) C₄

(0.3,0.4,0.5) (0.4,0.5,0.6) (0.5,0.6,0.7) (0.4,0.5,0.6) (0.2,0.3,0.4) C₅

(0.2,0.3,0.4) (0.4,0.5,0.6) (0.5,0.6,0.7) (0.4,0.5,0.6) (0.25,0.3,0.35) C₆

(0.1,0.2,0.3) (0.15,0.2,0.25) (0.2,0.3,0.4) (0.1,0.2,0.3) (0.1,0.2,0.3) C₇

(0.1,0.2,0.3) (0.15,0.2,0.25) (0.25,0.35,0.45) (0.15,0.25,0.35) (0.2,0.3,0.4) C₈

(0.3,0.4,0.5) (0.6,0.7,0.8) (0.5,0.6,0.7) (0.4,0.5,0.6) (0.2,0.3,0.35) E₁

(0.3,0.4,0.55) (0.5,0.6,0.7) (0.5,0.55,0.6) (0.4,0.5,0.6) (0.3,0.35,0.4) E₂

(0.4,0.45,0.5) (0.5,0.6,0.7) (0.4,0.5,0.6) (0.2,0.3,0.4) (0.25,0.3,0.35) E₃

(0.35,0.45,0.55) (0.6,0.7,0.8) (0.5,0.6,0.7) (0.3,0.4,0.5) (0.2,0.25,0.35) E₄

(0.4,0.5,0.6) (0.6,0.7,0.8) (0.4,0.5,0.6) (0.3,0.35,0.45) (0.25,0.3,0.35) E₅

(0.1,0.2,0.3) (0.2,0.3,0.4) (0.15,0.25,0.35) (0.2,0.3,0.4) (0.2,0.35,0.4) E₆

(0.1,0.2,0.3) (0.2,0.3,0.4) (0.2,0.25,0.3) (0.1,0.2,0.3) (0.15,0.2,0.3) E₇

(0.2,0.3,0.4) (0.3,0.4,0.5) (0.2,0.25,0.3) (0.1,0.2,0.35) (0.1,0.15,0.2) E₈

(0.2,0.3,0.4) (0.1,0.2,0.3) (0.15,0.2,0.3) (0.1,0.2,0.3) (0.15,0.2,0.25) M₁

(0.4,0.5,0.6) (0.25,0.35,0.45) (0.15,0.2,0.25) (0.1,0.15,0.2) (0.2,0.3,0.4) M₂

(0.7,0.8,0.9) (0.5,0.6,0.7) (0.45,0.5,0.55) (0.3,0.4,0.5) (0.2,0.3,0.45) M₃

(0.4,0.5,0.6) (0.3,0.4,0.5) (0.2,0.3,0.4) (0.25,0.3,0.35) (0.2,0.35,0.4) M₄

(0.2,0.3,0.4) (0.15,0.2,0.25) (0.2,0.25,0.3) (0.2,0.3,0.4) (0.2,0.25,0.3) M₅

(0.4,0.5,0.6) (0.3,0.4,0.5) (0.25,0.3,0.35) (0.2,0.3,0.4) (0.2,0.25,0.3) M₆

(0.5,0.6,0.7) (0.4,0.5,0.6) (0.2,0.3,0.4) (0.25,0.3,0.4) (0.15,0.2,0.25) M₇

(0.6,0.7,0.8) (0.5,0.6,0.7) (0.3,0.4,0.5) (0.15,0.2,0.35) (0.2,0.3,0.4) M₈

Management M = (0.1,0.2,0.3)	Financial E = (0.25,0.3,0.35)	Customer characteristics C = (0.2,0.25,0.3)	Feasibilities factors F = (0.1,0.15,0.2)	Carrier and education background J = (0.15,0.2,0.2)	Main factors Secondary
(0.2,0.25,0.3)	(0.25,0.3,0.35)	(0.2,0.3,0.4)	(0.1,0.15,0.2)	(0.1,0.2,0.3)	J₁
(0.25,0.3,0.35)	(0.3,0.4,0.5)	(0.25,0.35,0.45)	(0.15,0.2,0.25)	(0.15,0.25,0.35)	J₂
(0.3,0.35,0.4)	(0.35,0.4,0.45)	(0.3,0.4,0.5)	(0.25,0.3,0.35)	(0.25,0.3,0.35)	J₃
(0.25,0.3,0.35)	(0.3,0.35,0.4)	(0.25,0.3,0.35)	(0.2,0.25,0.3)	(0.2,0.25,0.3)	J₄
(0.2,0.25,0.3)	(0.15,0.2,0.3)	(0.1,0.15,0.2)	(0.15,0.2,0.25)	(0.15,0.2,0.25)	J₅
(0.1,0.15,0.2)	(0.05,0.1,0.15)	(0.05,0.15,0.2)	(0.1,0.15,0.2)	(0.1,0.15,0.2)	J₆
(0.1,0.15,0.2)	(0.05,0.1,0.15)	(0.1,0.15,0.2)	(0.05,0.1,0.15)	(0.05,0.1,0.15)	J₇
(0.2,0.3,0.4)	(0.2,0.3,0.4)	(0.25,0.35,0.45)	(0.2,0.3,0.4)	(0.3,0.4,0.5)	J₈
(0.4,0.5,0.6)	(0.15,0.25,0.35)	(0.2,0.3,0.5)	(0.3,0.4,0.5)	(0.2,0.3,0.4)	F₁
(0.4,0.5,0.6)	(0.25,0.35,0.45)	(0.2,0.35,0.4)	(0.35,0.45,0.55)	(0.25,0.3,0.35)	F₂
(0.5,0.6,0.7)	(0.2,0.3,0.35)	(0.25,0.3,0.35)	(0.4,0.5,0.6)	(0.2,0.3,0.4)	F₃
(0.4,0.5,0.6)	(0.25,0.35,0.45)	(0.2,0.3,0.4)	(0.4,0.5,0.6)	(0.4,0.45,0.5)	F₄
(0.45,0.5,0.55)	(0.35,0.45,0.55)	(0.3,0.4,0.5)	(0.4,0.5,0.6)	(0.35,0.4,0.45)	F₅
(0.6,0.65,0.7)	(0.4,0.5,0.6)	(0.5,0.6,0.7)	(0.6,0.7,0.8)	(0.4,0.5,0.6)	F₆
(0.5,0.55,0.6)	(0.15,0.2,0.25)	(0.2,0.3,0.4)	(0.2,0.3,0.4)	(0.35,0.45,0.55)	F₇
(0.6,0.7,0.8)	(0.25,0.35,0.45)	(0.3,0.4,0.5)	(0.4,0.5,0.6)	(0.3,0.4,0.5)	F₈
(0.1,0.2,0.3)	(0.15,0.25,0.35)	(0.2,0.3,0.4)	(0.15,0.3,0.35)	(0.2,0.3,0.35)	C₁
(0.2,0.3,0.4)	(0.2,0.3,0.4)	(0.25,0.3,0.35)	(0.2,0.25,0.3)	(0.2,0.25,0.3)	C₂
(0.15,0.25,0.35)	(0.25,0.35,0.4)	(0.3,0.4,0.5)	(0.25,0.35,0.45)	(0.2,0.3,0.4)	C₃
(0.2,0.3,0.4)	(0.1,0.2,0.3)	(0.2,0.3,0.4)	(0.1,0.2,0.3)	(0.15,0.25,0.35)	C₄
(0.3,0.4,0.5)	(0.4,0.5,0.6)	(0.5,0.6,0.7)	(0.4,0.5,0.6)	(0.2,0.3,0.4)	C₅
(0.2,0.3,0.4)	(0.4,0.5,0.6)	(0.5,0.6,0.7)	(0.4,0.5,0.6)	(0.25,0.3,0.35)	C₆
(0.1,0.2,0.3)	(0.15,0.2,0.25)	(0.2,0.3,0.4)	(0.1,0.2,0.3)	(0.1,0.2,0.3)	C₇
(0.1,0.2,0.3)	(0.15,0.2,0.25)	(0.25,0.35,0.45)	(0.15,0.25,0.35)	(0.2,0.3,0.4)	C₈
(0.3,0.4,0.5)	(0.6,0.7,0.8)	(0.5,0.6,0.7)	(0.4,0.5,0.6)	(0.2,0.3,0.35)	E₁
(0.3,0.4,0.55)	(0.5,0.6,0.7)	(0.5,0.55,0.6)	(0.4,0.5,0.6)	(0.3,0.35,0.4)	E₂
(0.4,0.45,0.5)	(0.5,0.6,0.7)	(0.4,0.5,0.6)	(0.2,0.3,0.4)	(0.25,0.3,0.35)	E₃
(0.35,0.45,0.55)	(0.6,0.7,0.8)	(0.5,0.6,0.7)	(0.3,0.4,0.5)	(0.2,0.25,0.35)	E₄
(0.4,0.5,0.6)	(0.6,0.7,0.8)	(0.4,0.5,0.6)	(0.3,0.35,0.45)	(0.25,0.3,0.35)	E₅
(0.1,0.2,0.3)	(0.2,0.3,0.4)	(0.15,0.25,0.35)	(0.2,0.3,0.4)	(0.2,0.35,0.4)	E₆
(0.1,0.2,0.3)	(0.2,0.3,0.4)	(0.2,0.25,0.3)	(0.1,0.2,0.3)	(0.15,0.2,0.3)	E₇
(0.2,0.3,0.4)	(0.3,0.4,0.5)	(0.2,0.25,0.3)	(0.1,0.2,0.35)	(0.1,0.15,0.2)	E₈
(0.2,0.3,0.4)	(0.1,0.2,0.3)	(0.15,0.2,0.3)	(0.1,0.2,0.3)	(0.15,0.2,0.25)	M₁
(0.4,0.5,0.6)	(0.25,0.35,0.45)	(0.15,0.2,0.25)	(0.1,0.15,0.2)	(0.2,0.3,0.4)	M₂
(0.7,0.8,0.9)	(0.5,0.6,0.7)	(0.45,0.5,0.55)	(0.3,0.4,0.5)	(0.2,0.3,0.45)	M₃
(0.4,0.5,0.6)	(0.3,0.4,0.5)	(0.2,0.3,0.4)	(0.25,0.3,0.35)	(0.2,0.35,0.4)	M₄
(0.2,0.3,0.4)	(0.15,0.2,0.25)	(0.2,0.25,0.3)	(0.2,0.3,0.4)	(0.2,0.25,0.3)	M₅
(0.4,0.5,0.6)	(0.3,0.4,0.5)	(0.25,0.3,0.35)	(0.2,0.3,0.4)	(0.2,0.25,0.3)	M₆
(0.5,0.6,0.7)	(0.4,0.5,0.6)	(0.2,0.3,0.4)	(0.25,0.3,0.4)	(0.15,0.2,0.25)	M₇
(0.6,0.7,0.8)	(0.5,0.6,0.7)	(0.3,0.4,0.5)	(0.15,0.2,0.35)	(0.2,0.3,0.4)	M₈

3.5 Separation of information to training and testing sets

The information collected from the previous stage should include all the effective and suitable information for decision making. Also this information has to be gathered in one place in order to select training and testing sets among them randomly. The training process in NN includes considering all of the information and using them for predicting characteristics and or behaviors of them in order to produce training and testing sets. For NN, it is ideal to generate training sets from each output, which is usually not feasible. On these bases, researchers in NN problems consider 20 to 30 percent of the inputs as testing set and 70 to 80 percent as training set [45]. In this research 75 percent (300 cases) of input is used for training set and 25 percent for testingset.

4 Selecting a suitable architecture for network

Selecting an optimum NN architecture is one of the research area which is still under investigation. In general, researchers do not agreed on ideal network architecture. Also they have different views on the number of middle layers and neurons inside each layer. As an example, Kaastra and Milton in their research show that the existence of one middle layer in NN is capable of modeling most of the functions and problems. Also in their research it is emphasized that the number of neurons of this layer is better to be, at most, equal to square root of multiplication of number of input and output neurons [46]. Multi layers perceptron network with back propagation training is basically formed from two main paths. In the forward path, the input vector is applied to the network and its effect is distributed from the middle layers to the output layers. The output vector, which is formed at the output layer, would be the actual network solution. In this path, the network parameters are considered fixed and without variation. In the backward path, the network parameters would vary and are adjusted. These adjustments are carried out based on the error correction rule. The error vector is equal to the difference between the desired answer vectors and the actual answer The amount of error which is calculated in the output layer is distributed all over the network through network layers. In this error distribution, the network parameters are adjusted so that the actual answer gets closer to the desired answer. To determine the network architecture, the function of neurons activity, the learning rules, the number of hidden layers, the number of neurons in each layer, and the rate of learning in each layer have to bespecified.

The main learning rule was presented by Rumelhart, Hinton and Williams (1986) and was named “the delta rule.” This learning rule includes three stages; outputs, comparison of actual and desired output, and adjustment of weights and bias values in an iteration process. In this operation, difference between actual and desired output is minimized [47].

The main issue in network architecture is determining the number of middle layers, and neurons in each hidden layer. If there is more than one hidden layer, the learning time will increase and the learning algorithm will be more complicated with more calculations. Also the less number of neurons in each hidden layer would lead to a better generalization of the networks into new problems. Existence of a hidden layer can simulate the conversion functions into a simple learning algorithm.

In this paper, a constrictive method is used for determining the number of layers. In this method, the inputs are directly connected to the outputs. The weights are trained so that the errors become a fixed value. Then a hidden layer with one neuron is created and the training activity is repeated. When increasing the number of hidden layers and their neurons does not cause any improvement, the process will be ended. In this case, the last added layer or neuron will be deleted. In this work, the least obtained network error is a hidden layer containing five neurons. This network also has 40 input neurons and one output neuron. The important point is that the obtained architecture is matched with AHP as shown in Fig. 2. That is, the number of neurons in the middle layer is equal to the clusters which can be classified to secondary factors in thoseclusters.

The learning rate is the last key of decision making. Usually, learning rate starts with a large value and close to one. If the error graph in output layer has many variations, either high or low, it can be concluded that the learning rate is optimum and has to be reduced with one ratio for all layers [45]. In this work, the learning rate is started with 0.9. Then, because of high variation in output layer, the learning rate is reduced, until it reaches to 0.7. At this stage the error graph shows the best status. Figure 3 shows its neural network graph.

Fig.3

The neural network graph.

5 Case study data for NN training

NN training includes presenting a set of information through matching weights with bias values to generate a desired output for each input. Selection of the suitable network architecture and the proper starting time can reduce the training network time and data requirements. The network which is obtained through constructive method and AHP contains 40 inputs and one output and a middle layer with 5 neurons. The primarily NN weights are analyzed by a random method, and by AHP. Finally, the AHP weights are used because of their better performance in terms of time and data requirements. Each set of input-output, can take one status, excellent, good, fair, poor, or very poor. The rules used in this paper is based on five level Likert scale in which the bank customers are classified into five groups.

Each output is in a fuzzy number format, which has to be transformed to one of the above statuses. For defining the customer credibly status, the following steps have to be carried out:

1. Determining the difference between customer credibly fuzzy number and each status options. $\begin{matrix} = \frac{1}{3} [{(a_{1} - b_{1})}^{2} + {(a_{2} - b_{2})}^{2} + {(a_{3} - b_{3})}^{2}] \end{matrix}$

2. Matching customer credibly fuzzy number and the status options. $\begin{matrix} u & = & min {d (A_{i}, E), d (A_{i}, G), d (A_{i}, F), \\ d (A_{i}, P), d (A_{i}, VP)} \end{matrix}$

3. Determining the customer status using decision making rules. $\begin{matrix} Rule 1 : If u = d (A_{i}, E) then Evaluation \\ = Excellent \\ Rule 2 : If u = d (A_{i}, G) then Evaluation = Good \\ Rule 3 : If u = d (A_{i}, F) then Evaluation = Fair \\ Rule 4 : If u = d (A_{i}, P) then Evaluation = Poor \\ Rule 5 : If u = d (A_{i}, VP) then Evaluation \\ = VeryPoor \end{matrix}$

6 Training, testing and executing network

The first stage in network training is defining the initial NN parameters’ values. It is obvious that a right selection could be a great help for faster convergence training algorithm. Therefore, in the first step, the initial values for NN parameters should be provided. The initial parameters for each NN include bias values and the inputs weights. In this paper, for learning the value rate is assumed 0.7, and AHP is used to generate input vector weights. Also for bias values, numbers between 0 and 1 are selected randomly. The NN using AHP weights and using random values for input variables are compared. The results showed the usage of AHP weights would speed up the calculations and give more accurateanswers.

Second training step uses one input and calculates the output as follows: $\begin{matrix} u_{j + 1} = u_{j} + b_{j} \times 1 u_{j} = \sum_{i = 1}^{22} w_{ij} . O_{pi} \\ u_{k} = \sum_{j = 2}^{5} w_{jk} O_{pi} u_{k + 1} = u_{k} + b_{k} \times 1 \end{matrix}$

Where u _j is the sum of neuron’s j inputs in the hidden layer. o _p i is the input to neuron in step p, w _i j is the weight of input neuron j and b _j is neuron’s j bios value in the hidden layer. Also u _k is the sum of inputs related to neuron’s k of the outer layer. Therefore o _p i is the input to neuron in step p, w _j k is the weight of input values to neuron k and the bias value of neuron’s k of the outer layer.

For producing outputs through each neuron, the summation of inputs (uj) is given to the transfer function. This function would convert the summations into numerical range of zero to one. $Y = \frac{1}{1 + e^{- u}}$

If the actual value of the output neuron and its ideal value are not equal, an error message will be given. In this stage with one backward movement and modifying the bias values and weights, the network tries to reduce or eliminate error.

In the third step, the error will be calculated. For calculating the outer layer error, the mean square error (MSE) method is used. $EP = \frac{1}{n} \sum_{i = 1}^{n} (T_{pk} - o_{pk})^{2}$

T _p k is the ideal output for neuron K in the outer layer and step P, and o _p k is the actual output of neuron k in the outer layer, and step p.

If any error in the outer layer is recognized by changing the values of weights and bias, the output error has to be reduced as much as possible. The simplest and most productive way to update the network weights is by using the steepest descent in direction of gradient vector. $W_{i} (new) = w_{i} (old) + 0 / 7 (Y_{i} - Y_{i}^{0.5 em ⌢})$

Y _i is the actual output value and $Y_{i}^{0.5 em ⌢}$ is the value of the desired output.

After the training stage, the network has to be tested. There would be no error amendment in the testing stage. If during the testing time, the network gives a correct answer, then the work is over; otherwise the training process has to be started again. In this research the network with AHP weights in 20 rounds and without AHP weights in 250 rounds is trained and reached to optimized status.

7 A numerical example

In this section forward and backward operation, calculation of transfer function, and distribution and amendment of NN training weights method is explained through a numerical example. Assume the secondary factors for a customer after filling questionnaire, or being interviewed are as shown in Table 3.

Table 3
The input information of a customer

Management Financial/economical Customer characteristics Feasibility factors Education and carrier history

M1 = fair E1 = good C1 = good F1 = good J1 = good

M2 = fair E2 = good C2 = good F2 = good J2 = good

M3 = excellent E3 = good C3 = good F3 = fair J3 = good

M4 = fair E4 = good C4 = fair F4 = good J4 = good

M5 = fair E5 = fair C5 = fair F5 = good J5 = fair

M6 = good E6 = good C6 = fair F6 = fair J6 = excellent

M7 = good E7 = poor C7 = poor F7 = fair J7 = poor

M8 = good E8 = fair C8 = good F8 = good J8 = poor

Management	Financial/economical	Customer characteristics	Feasibility factors	Education and carrier history
M1 = fair	E1 = good	C1 = good	F1 = good	J1 = good
M2 = fair	E2 = good	C2 = good	F2 = good	J2 = good
M3 = excellent	E3 = good	C3 = good	F3 = fair	J3 = good
M4 = fair	E4 = good	C4 = fair	F4 = good	J4 = good
M5 = fair	E5 = fair	C5 = fair	F5 = good	J5 = fair
M6 = good	E6 = good	C6 = fair	F6 = fair	J6 = excellent
M7 = good	E7 = poor	C7 = poor	F7 = fair	J7 = poor
M8 = good	E8 = fair	C8 = good	F8 = good	J8 = poor

By using Table 1, the fuzzy numbers in Table 3 are determined and multiplied by each column of Table 2 using equation (a ₁, b ₁, c ₁). (a ₂, b ₂, c ₂) = (a ₁. a ₂, b ₁. b ₂, c ₁. c ₂) and then they are added together. The results of the above operation are shown in the first row of Table 4. These numbers are put in transfer function $Y = \frac{1}{1 + e^{- x}}$ , which will form the third row of Table 4.

Table 4

The results of fuzzy NN output

Management	Financial/ economical	Customer characteristics	Feasibility factors	Education and carrier
(2.5,3,3.5)	(1.5,2.5,3.7)	(2.6,3,3.7)	(1.5,2.1,2.7)	(2.2,2.5,3.8)	1
(0.92,0.95,0.97)	(0.82,0.92,0.98)	(0.93,0.95,0.98)	(0.82,0.89,0.94)	(0.9,0.95,0.98)	2

The Fuzzy number in second row of Table 4 multiplies by the fuzzy number of first row of Table 2 and then they will be separated from each other. The results of the operation form the fuzzy number (0.85, 0.90, 0.95). This fuzzy number is put in function $Y = \frac{1}{1 + e^{- x}}$ and is changed to (0.70,.0.71,0.72). This fuzzy number has to be transferred to verbal statement based on steps explained in section 5. $\begin{array}{l} d (A_{i}, E) = & \frac{1}{3} [{(0 .75 - 0 .85)}^{2} + (1 - 0 {.9)}^{2} \\ + {(1 - 0 .95)}^{2} = 0 .007 \\ d (A_{i}, G) = & \frac{1}{3} [{(0 .5 - 0 .85)}^{2} + (0 .75 - 0 {.9)}^{2} \\ + {(1 - 0 .95)}^{2} = 0 .062 \\ d (A_{i}, F) = & \frac{1}{3} [{(0 .25 - 0 .85)}^{2} + (0 .5 - 0 {.9)}^{2} \\ + {(0 .75 - 0 .95)}^{2} = 0 .45 \\ d (A_{i}, P) = & \frac{1}{3} [{(0 - 0 .85)}^{2} + (0 .25 - 0 {.9)}^{2} \\ + {(0 .5 - 0 .95)}^{2} = 0 .46 \\ d (A_{i}, V) = & \frac{1}{3} [[(0 - 0 {.85)}^{2} + (0 - 0 {.9)}^{2} \\ + {(0 .25 - 0 .95)}^{2} = 0 .67 \end{array}$

The status of the customer becomes “excellent” by selecting the least value of above numbers (d(A_i ,E) = 0.007). Now, this status has to be compared with the “good” status of the customer.

To adjust and amend the weights, three rules have been used. These rules are as follows: if the result is above actual value, the weight will be reduced and if it is below actual value the weights will be increased, and otherwise there will be no change. $I f E v a l u a t i o n > E s t i m a t o r t h e n$

$\begin{array}{l} w i (n e w) = w i (o l d) + 0.7 (y - \overset{⌢}{y}) \\ I f E v a l u a t i o n < E s t i m a t o r t h e n \end{array}$

$\begin{array}{l} w i (n e w) = w i (o l d) + 0.7 (y - \overset{⌢}{y}) \\ I f E v a l u a t i o n = E s t i m a t o r t h e n \end{array}$

$w i (n e w) = w i (o l d)$

In this situation since the estimated status is excellent and the actual status is good, situation b has occurred. Therefore, the value of new weights is cal-culated by equation: $w i (n e w) = w i (o l d) + 0.7 (y - \overset{⌢}{y}) .$ .

That is the weight values should be less in order to the estimated result gets closer to actual value.

In this stage the existing error is distributed to the previous layers through a backward path and based on the hierarchy of NN.

Management:

0.042(0.1, 0.2, 0.3) = (0.004, 0.008, 0.012)

Financial and economical:

0.042(0.25, 0.3, 0.35) = (0.01, 0.012, 0.015)

Customer characteristic:

0.042(0.2, 0.25, 0.3) = (0.008, 0.01, 0.012)

Feasibility:

0.042(0.1, 0.15, 0.2) = (0.004, 0.006, 0.008)

Carrier and educational background:

0.042(0.15, 0.2, 0.25) = (0.006, 0.008, 0.01)

In second stage error distribution, the error value should be distributed from second layer to third layer. For this operation the fuzzy numbers (0.004, 0.008, 0.012), (0.01, 0.012, 0.015), (0.008, 0.01, 0.012), (0.004, 0.006, 0.008), (0.006, 0.008, 0.01) should be multiplied by first, second, third, forth, and fifth column respectively. For example error distribution for inputs is as follows:

J1M: (0.004, 0.008, 0.012)(0.2,0.25,0.3)

=(0.001,0.002,0.004)

J1E: (0.01,0.012,0.015) (0.25,0.3,0.35)

=(0.002,0.004,0.005)

J1C: (0.008,0.01,0.012) (0.2,0.3,0.4)

=(0.002,0.003,0.005)

J1F: (0.004,0.006,0.008) (0.1,0.15,0.2)

=(0.0004,0.0009,0.002)

J1J: (0.006,0.008,0.01)(0.1,0.2,0.3)

=(0.0006,0.002,0.003)

Adjustment of weights is determined from equation W_i(new) = W_i(old) + 0.7(y−y).

For example wi of management at first level is adjusted as below:

w_i (new) = (0.1, 0.2, 0.3) − 0.7(0.04, 0.08, 0.012)

= (0.097, 0.194, 0.292)

This example reached to the desired answer after 20 rounds. Table 5 compares the number of stages, solution time, and response accuracy for ANN and ANN with AHP.

Table 5

Results comparison

Method	Number of stages	Solution Time (s)	Accuracy	No. of Correct answer
ANN	1237	108206	0.83	332
AHP and ANN	20	1756	W).95	380
Improvement	98 %	98%	12%	12%

8 Conclusions and future researches

In this study, a credit measurement system to recognize customers’ behavioral patterns and then to predict customers’ behavior are designed and imple-mented in large credit market. Also by using weights obtained from AHP in NN architecture and training, ability and results of NN were improved considerably. Using NN and AHP in customer credibly clustering is promising in better forecasting of customer behavior with less data, time, and cost. Capability of NN in modeling of various functions and training, when used with AHP, showed that it will increase the speed and accuracy of NN. Also, in this work the AHP hierarchy is used as network architecture, and weights resulted from AHP is used as primary weights in NN. To test the model in a real life situation, it is applied to Iranian National Bank. The proposed method (AHP and ANN), when compared to the normal ANN, shows an increase in speed and accuracy of respectively 12% and 98%, For future research the adoption of number of neurons in middle layers with the number of clusters that can be classified in secondary factors and sensitivity analysis for determining the effect of each inputs elements on outputs elements are recommended.

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